Corrections to tribimaximal neutrino mixing: renormalization and Planck scale effects

Abstract

We study corrections to tribimaximal (TBM) neutrino mixing from Renormalization Group (RG) running and from Planck scale effects. We show that while the RG effects are negligible in the Standard Model (SM), for quasidegenerate neutrinos and large tan β in the Minimal Supersymmetric Standard Model (MSSM) all three mixing angles may change significantly. In both these cases, the direction of the modification of θ₁₂ is fixed, while that of θ₂₃ is determined by the neutrino mass ordering. The Planck scale effects can also change θ₁₂ up to a few degrees in either direction for quasidegenerate neutrinos. These effects may dominate over the RG effects in the SM and in the MSSM with small tan β. The usual constraints on neutrino masses, Majorana phases or tan β stemming from RG running arguments can then be relaxed. We quantify the extent of Planck scale effects on the mixing angles in terms of “mismatch phases” which break the symmetries leading to TBM. In particular, we show that when the mismatch phases vanish, the mixing angles are not affected in spite of the Planck scale contribution. Similar statements may be made for μ–τ symmetric mass matrices.